How do you factor a cubic polynomial if the factors of constant d in f(x) = ax^3 + bx^2 + cx + d is not a whole number?

For example, I know the method of taking the factors of d, testing out which ones equal to zero to obtain a linear factor, and performing synthetic or long division to get the other (quadratic) factor.

However, this method does not work for something like f(x) = 2x^3 + 7x^2 + 6x - 5, which factors out into f(x) = (2x - 1)(x^2 + 4x + 5)

So what method can you use to factor a cubic polynomial like that?